Rigid Transform

Fixed spatial relationship between frames

• Library:

• Simscape / Multibody / Frames and Transforms

• 

Description

This block applies a time-invariant transformation between two frames. The transformation rotates and translates the follower port frame (F) with respect to the base port frame (B). Connecting the frame ports in reverse causes the transformation itself to reverse. The frames remain fixed with respect to each other during simulation, moving only as a single unit. Combine Rigid Transform and Solid blocks to model compound rigid bodies.

Ports

Frame

B — Base frame

frame

Frame with respect to which you specify the transforms.

F — Follower frame

frame

Frame to which you apply the transforms.

Parameters

Rotation: Method — Method for specifying the rotation transform

None (default) | Aligned Axes | Standard Axis | Arbitrary Axis | Rotation Sequence | Rotation Matrix

Method to use to specify the rotation transform between the base and follower frames. The table summarizes the available options.

Method	Description
None	Constrain the base and follower frames to share the same orientation.
Aligned Axes	Set frame rotation by aligning two follower frame axes with two base frame axes.
Standard Axis	Specify frame rotation as an angle about a standard axis (x, y, or z).
Arbitrary Axis	Specify frame rotation as an angle about a general [x, y, z] axis.
Rotation Sequence	Specify frame rotation as a sequence of three elementary rotations.
Rotation Matrix	Specify frame rotation as a right-handed orthogonal rotation matrix.

Aligned Axes

Select two pairs of base-follower frame axes.

Parameter	Description
Pair 1	First pair of base-follower frame axes to align.
Pair 2	Second pair of base-follower frame axes to align. Axis choices depend on Pair 1 axis selections.

Standard Axis

Select a standard rotation axis, resolved in the base frame, and specify the follower frame rotation angle.

Parameter	Description
Axis	Standard rotation axis (X, Y, or Z) resolved in the base frame.
Angle	Follower frame rotation angle about the rotation axis with respect to the base frame.

Arbitrary Axis

Select a general 3-D rotation axis, resolved in the base frame, and specify the follower frame rotation angle.

Parameter	Description
Axis	General rotation axis [X Y Z] resolved in the base frame.
Angle	Follower frame rotation angle about the rotation axis with respect to the base frame.

Rotation Sequence

Specify a sequence of three elementary rotations about the selected permutation of x, y, and z axes. These rotation sequences are also known as Euler and Tait-Bryan sequences. The rotations are those of the follower frame relative to the frame selected in the Rotate About parameter.

If you set the Rotate About parameter to Follower Frame, the follower frame rotates about its own axes. These axes change orientation with each successive rotation. If you set the Rotate About parameter to Base Frame, the follower frame rotates about the fixed base frame axes.

Parameter	Description
Rotation About	Frame whose axes to rotate the follower frame about.
Sequence	Sequence of axes about which to apply the elementary rotations.
Angles	Three-element vector with elementary rotation angles about the axes specified in the Sequence parameter.

Rotation Matrix

Specify the 3×3 transformation matrix of a proper rotation between the base and follower frames. The matrix must be orthogonal and have determinant +1. The default matrix is [1 0 0; 0 1 0; 0 0 1].

Translation: Method — Method for specifying the translation transform

None (default) | Cartesian | Standard Axis | Cylindrical

Method to use to specify the translation transform between the base and follower frames. The table summarizes the available options.

Method	Description
None	Make base and follower frames coincident. This method requires no parameters.
Cartesian	Specify a 3-D translation in terms of Cartesian coordinates
Standard Axis	Specify a 1-D translation along the X, Y, or Z axis
Cylindrical	Specify a 3-D translation in terms of cylindrical coordinates

Cartesian Axis

Specify the Offset of the follower frame with respect to the base frame. This is the 3-D translation vector that brings the base frame into coincidence with the follower frame. Select or enter a physical unit.

Standard Axis

Specify the offset of the follower frame with respect to the base frame along the base frame X, Y, or Z axis. Select or enter a physical unit.

Parameter	Description
Axis	Axis the follower frame translates along
Offset	Translation of the follower frame with respect to the base frame along the specified axis

Cylindrical

Specify in cylindrical coordinates the translation that brings the base frame into coincidence with the follower frame. Select or enter a physical unit.

Parameter	Description
Radius	Distance between the origin of the follower frame and the Z axis of the base frame. This is the cylindrical radius coordinate.
Theta	Rotation angle of the line connecting base and follower frame origins with respect to the base frame X axis. This is the cylindrical azimuth coordinate.
Z Offset	Distance between base and follower frame origins along the base frame Z axis. This is the cylindrical length coordinate.

Model Examples

Creating Frames Using Rigid Transforms

The correspondence of coordinate frames to connection lines and frame ports. It highlights the Rigid Transform block as the fundamental method to rigidly relate nonidentical frames. The network reference frame is the world frame, located at the center of the bottom face of the cube. The other frames are the frames at the eight vertices of the cube, one at the center of the top face, and two on the upper curved section.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.